well...

accepted

Acceptance is a basic human desire. A fair share of people don't seek it from society at large, but from their peers. Beyond that, there are people who will do what do, no matter if it results in acceptance or not.

accomplished

Accomplishment implies success of some sort, which doesn't account for the issue of trying. Success is admirable, but failure, in many cases, can be just as important, especially as a vehicle for learning. Also, a person's definition of success may be vastly different than another person's. For example, compare an accomplished musician to an accomplished activist. It's too difficult to separate personal goals from altruistic goals, or developmental goals from intellectual goals, etc.

accepted vs accomplished

Even though it might be better to be experienced as opposed to accomplished (to take account for failures as well as successes), I would rather be accomplished than accepted... at least in terms of this world. What is it to be accomplished before God, but not accepted by Him? In worldly terms, I feel it's better to have done something and not be accepted than to be accepted for doing nothing. It's an extreme way to look at it, but it's a hard comparison.

Jesus wasn't widely accepted in His time...